Spatiotemporal Variations and Characteristics of CO, H₂CO and HCN Emissions from Biomass Burning Monitored by FTIR Spectroscopy

Abstract

Studies of the impact of biomass burning and the emissions of trace gases from biomass burning, especially using long-term observations, are scarce in China. We utilize solar absorption spectra obtained via ground-based high-resolution Fourier transform infrared (FTIR) spectroscopy to retrieve the atmospheric total columns and vertical profiles of carbon monoxide (CO), formaldehyde (H₂CO), and hydrogen cyanide (HCN) in Hefei, China. Seasonal and interannual variability in the three gases from 2016 to 2022 are analyzed. Atmospheric CO shows significant seasonal variations, peaking during spring and winter, and declining during summer, with a seasonal amplitude of 8.07 × 10¹⁷ molecules cm⁻² and a seasonal variability of 29.35%. H₂CO and HCN have similar seasonal patterns to each other, with high concentrations in summer and low concentrations in winter. The seasonal amplitude of H₂CO and HCN are 1.89 × 10¹⁶ molecules cm⁻² and 2.32 × 10¹⁵ molecules cm⁻², respectively, with a seasonal variability of 133.07% and 34.69%, respectively. The means of the annual variation rate for CO, H₂CO, and HCN are (−2.67 ± 2.88)% yr⁻¹, (2.52 ± 12.48)% yr⁻¹ and (−3.48 ± 7.26)% yr⁻¹, respectively. To assess the influence of biomass burning on the variations in column concentrations of the three gases, the correlation between CO, H₂CO, and HCN was analyzed. The months during which the monthly correlation coefficient between CO and H₂CO with HCN exceeds 0.8, and the fire radiative power (FRP) observed by satellites is larger than its monthly average are regarded as a biomass-burning occurrence in Anhui province. Additionally, the enhancement ratios of ΔH₂CO/ΔCO and ΔHCN/ΔCO were calculated for the periods impacted by the biomass burning. Finally, backward trajectory cluster analysis and the potential source contribution function (PSCF) calculation identified the air mass transport pathways and the potential source areas at the Hefei site.

1. Introduction

Biomass burning significantly contributes to atmospheric particulate matter, greenhouse gases, and pollution gases, thereby influencing air quality and global radiative forcing, as well as accelerating climate change [1,2,3,4]. Emissions from biomass burning release various trace gases, including carbon monoxide (CO), formaldehyde (H₂CO), and hydrogen cyanide (HCN) [5]. HCN has a lifetime of approximately 2–4 months, while CO persists for around two months [6,7]. H₂CO rapidly reacts with OH, NO₃, Br, and Cl, resulting in a typical persistence of several hours [8]. The primary sources of CO include fossil fuel combustion, biomass burning, and oxidation of hydrocarbons, including methane. CO is a significant tropospheric pollutant, functioning as an ozone precursor and an indirect greenhouse gas [9,10]. In the troposphere, CO is predominantly removed through oxidation by the hydroxyl radical (OH) [11], playing a crucial role in atmospheric chemistry by influencing the tropospheric oxidizing capacity [12]. H₂CO is released directly into the atmosphere through various sources, including anthropogenic emissions, such as industrial emissions and motor exhaust, biogenic emissions such as from living and decaying plants and seawater, and pyrogenic emissions such as burning of garbage, biomass fuels, and paddy stubble [13,14,15,16,17,18,19]. Direct emissions from biomass burning account for a minor part of the H₂CO budget, but biomass burning is an important local source, particularly during fire events. Additionally, H₂CO forms through the degradation of hydrocarbons and serves as an important intermediate in the oxidation of volatile organic compounds (VOCs) from biogenic, anthropogenic, and pyrogenic sources [20]. For atmospheric HCN, the main contributor is biomass burning [21]. The main sink for HCN is ocean uptake, with minor sinks including reactions with atmospheric hydroxyl radicals (OH) and O(¹D), and photolysis [22,23,24]. Because of its chemical inactivity and extended longevity, HCN is considered a reliable tracer for biomass-burning emissions [7,25]. Therefore, measurements of HCN are particularly useful for identifying the characteristics of atmospheric-gas variations driven by biomass burning.

Ground-based high-resolution Fourier transform infrared (FTIR) spectroscopy can precisely measure total columns of CO, H₂CO, HCN, and other trace gases [26,27,28]. Changes in atmospheric composition caused by biomass burning can be reflected by variations in CO, H₂CO, and HCN [29]. Combined measurements of CO and HCN aid in comprehending the transport of biomass-burning emissions [7,30]. Lutsch et al., (2020) utilized the data measured by FTIR at multiple sites to trace sources of atmospheric CO, HCN, and ethane (C₂H₆), highlighting the efficacy of ground-based FTIR in quantifying emissions from biomass burning [31]. Based on FTIR measurements conducted at the Xianghe station in China, Zhou et al. (2022) discovered a significant correlation between CO and various compounds such as acetylene (C₂H₂), C₂H₆, H₂CO, and HCN. By combining backward simulations based on the FLEXPART model and satellite observations, the researchers demonstrated that emissions from wildfires in northern Russia contributed to the elevated total columns of HCN in Xianghe [32].

Although some sites have utilized ground-based FTIR spectroscopy to analyze trace gases such as CO, H₂CO, and HCN to explore the impact of biomass burning on atmospheric composition, the study of the influence of biomass burning and the emissions of trace gases during biomass burning, especially using long-term observations, are relatively scarce in China. This study fills the knowledge gap by investigating the total column variations and interrelationships of CO, H₂CO, and HCN. In addition, the Hefei site is located in the northwestern suburb of Hefei City, which is in the Yangtze River delta region. Hefei city has suffered from heavy air pollution in recent years, due to rapidly growing industry, high levels of traffic, energy consumption, and biomass burning, so the study of the effect of these sources on the variation of the pollution gases and taking measures to control pollution emissions are of great significance. Section 2 details the observation site, instruments, spectral retrieval methods, retrieval strategies, typical retrieval information, and error analysis. Section 3 discusses the seasonal variation and annual variation of CO, H₂CO, and HCN from 2016 to 2022, and calculates the enhancement ratio of H₂CO and HCN relative to CO in biomass-burning periods. Section 4 summarizes the conclusion of this study.

2. Measurements and Methods

2.1. Instruments and Site Description

The ground-based FTIR remote-sensing site in Hefei is situated at 31.91°N, 117.17°E, and 29 m above sea level, which is within the urban environment of this city in eastern China. Managed by the Key Laboratory of Environmental Optics and Technology, the site has a rooftop solar tracker (A547N, Bruker, Billerica, MA, USA) and a high-resolution Fourier transform infrared spectrometer (Bruker IFS 125HR, Bruker, Billerica, MA, USA) among its instruments. The instrument is specifically designed for atmospheric remote sensing on clear days, and it alternately collects mid-infrared (MIR) and near-infrared (NIR) solar absorption spectra. This spectrometer covers key absorption features of various atmospheric gases. Equipped with a Michelson interferometer, it has high spectral resolution and can precisely observe trace gases. The FTIR spectrometer works in conjunction with the automatic solar tracker, which aligns the instrument with the sun to ensure continuous and reliable data collection. Since September 2015, the observation site has also been equipped with a weather station (ZENO, Coastal Environmental Systems, Seattle, WA, USA) that records meteorological data [33,34]. The FTIR instrument uses an indium gallium arsenide (InGaAs) detector and a calcium fluoride (CaF₂) beam splitter to record NIR solar spectra (4000–11,000 cm⁻¹), with a spectral resolution of 0.02 cm⁻¹ [11,33]. For NIR spectra, the spectrum acquisition time is approximately 90 s. For MIR spectra (600–4500 cm⁻¹), it employs a potassium bromide (KBr) beam splitter, a mercury cadmium telluride (MCT) detector, and an indium antimonide (InSb) detector, achieving a spectral resolution of 0.005 cm⁻¹ [33,35]. The spectrum acquisition time is approximately 288 s. Multiple optical filters mounted in front of the detectors are employed to enhance the signal-to-noise ratio (SNR) of the retrieval spectra. Low-pressure HBr and HCl cells are used to maintain proper alignment of the interferometer and to monitor the instrument line shape (ILS) of the spectrometer [11,33,35].

2.2. The Retrieval Principles

The MIR spectra at the Hefei site are analyzed using the SFIT4 algorithm, which is an improved version of SFIT2 [6,36], to retrieve CO, H₂CO, and HCN profiles. The forward model ($F$) describes the physical processes of solar radiation interacting with the atmosphere, linking the parameter vector ($b$) representing atmospheric state and auxiliary/instrumental parameters with the state vector ($x$) and measurement vector ($\mathrm{y}$) from the measured solar absorption spectrum, as shown below:

$$Y=F\left(x,b\right)+\mathsf{\epsilon }$$

(1)

In this equation, $\mathsf{\epsilon }$ denotes the measurement noise, which includes random noise and retrieval uncertainty. This scenario presents an ill-posed problem, as nearly identical spectra ($y$) can be yielded by multiple atmospheric states ($x$). The ill-posed problem is mostly due to a lack of vertical resolution. To mitigate this issue, a cost function ($\mathrm{J}\left(x\right)$) is employed to constrain the solution state:

$$\mathrm{J}\left(x\right)={\left[y-F\left(x,b\right)\right]}^T{S}_{\epsilon }^{-1}\left[y-F\left(x,b\right)\right]+{\left[x-x_a\right]}^T{S}_R\left[x-x_a\right]$$

(2)

The discrepancy between the spectrum simulated under the defined atmospheric state ($x$) and the observed spectrum ($y$) is quantified in the first term, with $S_{\epsilon }$ being the measurement covariance matrix for $y-F\left(x,b\right)$. The regularization term corresponds to the second term. $S_R$ denotes the covariance matrix of the a priori, reflecting the uncertainty or confidence in the a priori estimate, and is used to define the strength and type of constraint that constrain the a priori state ($x_a$) and the atmospheric state ($x$). The solution is obtained by minimizing the cost function $\mathrm{J}\left(x\right)$. Since the FTIR measurement’s forward model is nonlinear, numerical methods are used to iteratively minimize the cost function. The iteration process for the (i + 1)th is described as follows:

$$x_{i+1}=x_a+G_i\left[y-F\left(x_i,b\right)+K_i(x_i-x_a)\right]$$

(3)

where G represents the gain matrix, capturing the sensitivity of the measurement vector ($y$) to variations in the atmospheric state ($x$) as represented by the Jacobian matrix ($\mathrm{K}$). The relationship between the true state vector ($x$) and the retrieved state vector ($\widehat{x}$) can be formulated as follows [37]:

$$\widehat{x}-x_a=A\left(x-x_a\right)+{\epsilon }_x$$

(4)

In this equation, $A$ is the matrix of averaging kernel ($A=KG$). $A$ quantifies the degrees of freedom for signal (DOFs), with its trace indicating the vertically independent information derived from the measurements. ${\epsilon }_x$ denotes the error terms.

From retrieval results, total column ($C_r$) can be calculated as follows:

$$C_r=P{C}_{air}·\widehat{x}=T{C}_a+A_c·\left(P{C}_t-P{C}_a\right)+{\mathsf{\epsilon }}_c$$

(5)

In this equation, $P{C}_a$, $P{C}_t$, and $P{C}_{air}$ denote the a priori, the target species’ true profile, and the profile array of dry air partial column, respectively; ${\mathsf{\epsilon }}_c$ is the retrieval uncertainty of the total column; $A_c$ stands for the averaging kernel of the total column; $T{C}_a$ represents the a priori total column of the target species [32,38]. This comprehensive process ensures accurate retrieval of atmospheric profiles from MIR spectra.

2.3. Retrieval Strategies

The retrieval strategy determines the accuracy of the solar absorption spectrum retrieval results. Trace gases have different absorption characteristics in different spectral bands. The selected spectral window for retrieval should not only avoid the saturation of strong absorption lines but also avoid the signal of weak absorption lines being submerged by noise, so as to minimize the interference of other gases and solar spectral lines. A prior profile information and interference gas composition have an important influence on spectral retrieval. The spectral retrieval parameters of atmospheric CO, H₂CO, and HCN are set as shown in

Table 1. Spectral retrieval strategies parameter settings.

Species	CO	H2CO	HCN
Spectral windows(cm−1)	2057.70–2058.00	2763.42–2764.17	3268.02–3268.38
	2069.56–2069.76	2765.65–2766.00	3287.01–3287.48
	2157.50–2159.15	2778.15–2779.10	3299.40–3299.60
		2780.65–2782.00
Interfering gases	H2O, CO2, N2O, O3, OCS	CH4, HDO, N2O, O3	H2O, C2H2, O3, CH4
Retrieval software	SFIT4 V0.9.4.4
Spectroscopy	HITRAN 2008
T, P, and H2O profiles	NCEP
A priori information	WACCM v6
Surface meteorological data	Weather station
Atmospheric stratification	48 layers
Simulated height	0–120 km

. There are three retrieval windows for CO and HCN, and four for H₂CO. The spectroscopic signatures of the interfering gases were accounted for to minimize fitting residuals. H₂O and HDO are treated as distinct interfering species during retrieval, with line parameters sourced from the HITRAN 2008 database. The daily atmospheric temperature, pressure, and humidity a priori profiles are interpolated using reanalysis data from the National Centers for Environmental Prediction (NCEP) [39]. A priori profile data from version 6 of the Whole Atmosphere Community Climate Model (WACCAM) are used for CO, H₂CO, HCN, and other interfering gases except H₂O and HDO. The ground meteorological data are recorded by the weather station. The atmosphere is divided into 48 discrete layers from the surface to 120 km for model calculation [35,40,41].

2.4. Typical Retrieval Information

Table 2. Retrieval results of typical spectra.

Gas	Date	SZA	Total Column	RMS	DOFs
CO	13 January 2017	57.65°	3.03 × 1018	0.20%	4.58
H2CO	10 March 2018	46.56°	4.55 × 1015	0.20%	1.41
HCN	11 January 2018	65.71°	5.45 × 1015	0.12%	1.31

Unit of the total column is molecules cm⁻².

shows the retrieval results of the three gases from typical spectra. The spectrum for CO retrieval was collected at 02:46:23 UTC on 13 January 2017. During the measurement period, the solar zenith angle (SZA) was recorded as 57.65°. For H₂CO retrieval, the spectrum was collected at 02:15:24 UTC on 10 March 2018. The SZA was 46.56° during this measurement period. The spectrum for HCN retrieval was collected at 01:38:35 UTC on 11 January 2018. During this measurement period, the SZA was 65.71°. The total columns retrieved for CO, H₂CO, and HCN are 3.03 × 10¹⁸, 4.55 × 10¹⁵, and 5.45 × 10¹⁵, respectively. Figure 1, Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6 illustrate the results of spectral fitting in the microwindows, the averaging kernels, the retrieved vertical profile, and the DOFs of CO, H₂CO, and HCN. The averaged root-mean-square (RMS) error for CO, H₂CO, and HCN of the spectral fitting residual is 0.20%, 0.20%, and 0.12%, respectively. The RMS of the residuals of the three target gases are very small, indicating that the spectral fitting is good. The a priori profiles of CO and H₂CO closely resemble the retrieved profiles, while the retrieved concentrations of HCN are markedly higher in the troposphere compared to those in the a priori profile. The typical averaging kernel matrix for CO, H₂CO, and HCN is shown in Figure 4. Each CO layer exhibits higher sensitivity at about 18 and 80 km. H₂CO shows higher sensitivity below 50 km, decreasing to zero above 50 km. For HCN, maximum sensitivity for each layer occurs around 15 km, diminishing above 60 km. The trace of the averaging kernel provides an estimate of the vertical sensitivity of the retrieval, representing the DOFs [42]. The larger value indicates greater vertical information is achieved. The typical DOFs values of CO, H₂CO, and HCN are 4.58, 1.41, and 1.31, respectively, and the DOFs value of CO is the largest.

2.5. Retrieval Uncertainty

Taking potential errors into account, Equation (4) can be reformulated as follows:

$$\widehat{x}=x_a+A\left(x-x_a\right)+G{K}_b\left(b-\widehat{b}\right)+G_{\epsilon }$$

(6)

Here $x_a$ denotes a reference profile, ε represents the measurement noise, $K_b$ denotes the Jacobian matrix of model parameters, and $\widehat{b}$ represents estimated model parameters. $\widehat{x}$ is the linearized retrieved state.

Equation (6) forms the foundation of this analysis. The terms, respectively, account for smoothing errors, uncertainties in input or model parameters, and measurement noise [38]. The uncertainties in interfering species, target gas, and other retrieved parameters (such as wavenumber offset and slope) influence smoothing errors. Key parameters for model parameter errors include temperature, SZA, spectroscopy, and zero level offset (zshift). Measurement noise is assumed to be purely random [32]. The root mean square of these three types of errors was calculated to determine the total error.

The total retrieval error for a typical spectrum is calculated, and

Table 3. Random and systematic uncertainties for CO, H₂CO, and HCN retrieval.

Uncertainty [%]	CO		H2CO		HCN
	Systematic	Random	Systematic	Random	Systematic	Random
Target species	0.01	0.04	0.05	1.08	1.0	6.85
Retrieved parameters	0.002	0.002	0.16	0.16	1.72	1.72
Interfering species	0.01	0.01	0.1	0.67	0.1	0.99
Measurement error	/	0.11	/	5.82	/	5.21
SZA	0.42	0.42	0.64	0.64	0.006	0.006
Temperature	0.69	1.04	0.35	1.65	0.11	0.60
Zshift	0.20	0.20	0.09	0.09	0.02	0.02
Spectroscopy	1.24	/	2.60	/	2.31	/
Subtotal error	1.49	1.15	2.70	6.22	3.05	8.85
Total	1.88		6.78		9.35

shows the results. For CO, the total error is 1.88%, comprising a random error of 1.15% and a systematic error of 1.49%. The primary source of error is the model parameter error. For H₂CO, the total error is 6.78%, comprising a random error of 6.22% and a systematic error of 2.70%, with measurement error being the main contributor. The total error of HCN is 9.35%, of which the random error is 8.85% and the systematic error is 3.05%. The measurement error and smoothing error are the main sources of error.

3. Results

3.1. The Variation of Atmospheric CO, H₂CO, and HCN

Figure 7 displays the time series and daily mean of CO, H₂CO, and HCN total column measured at the Hefei site from 2016 to 2022. The data gap of the HCN total column from June to September is due to the high humidity in summer when the interference of water vapor affects the retrieval of HCN, thus some data with poor quality are filtered out. To better visualize the seasonal variation and annual trend, the time series in Figure 7d–f is fitted using a lowpass filtering fast Fourier transform (FFT) technique. The following is the FFT function $f\left(x\right)$:

$$f\left(x\right)=Hx+C+{\sum }_{k=1}^3\left(a_{2k-1}\cos \left(2\pi kx\right)+a_{2k}\sin \left(2\pi kx\right)\right)$$

(7)

where $x$, $H$, and $C$ denotes the time fraction annually, the trend of each year, and the intercept, respectively. Additionally, $a_1$ to $a_6$ represent the coefficient of sine/cosine harmonic [40,43].

CO, H₂CO, and HCN show an obvious seasonal variation, as shown in Figure 7, and the monthly variation in Figure 8. The CO reaches its peak in February and its lowest point in July, showing a seasonal amplitude of 8.07 × 10¹⁷ molecules cm⁻² and a seasonal variability of 29.35%. Atmospheric CO column concentrations peak during spring (March, April, and May) and winter (December, January, and February), with the lowest levels observed during summer (June, July, and August). Conversely, the total column of H₂CO is highest in summer and lowest in winter. July recorded the highest monthly mean value of H₂CO, while January had the lowest. The seasonal amplitude is 1.89 × 10¹⁶ molecules cm⁻², with a seasonal variation of 133.07%. The column concentration of HCN is higher during summer (in June) and lower during winter. The maximum monthly mean value of HCN occurred in June, while the minimum occurred in December, reflecting a seasonal amplitude of 2.32 × 10¹⁵ molecules cm⁻², and the seasonal variation was 34.69%.

Table 4. The mean and annual variation of the total column for CO, H₂CO, and HCN.

	CO		H2CO		HCN
Year	Mean (×1018)	Variation (%)	Mean (×1016)	Variation (%)	Mean (×1015)	Variation (%)
2016	3.04 ± 0.61	/	1.48 ± 0.86	/	7.87 ± 1.46	/
2017	2.82 ± 0.52	−7.28	1.50 ± 0.78	1.27	6.62 ± 0.78	−15.87
2018	2.74 ± 0.49	−2.83	1.41 ± 0.65	−6.06	6.33 ± 0.90	−4.40
2019	2.81 ± 0.39	2.40	1.30 ± 0.65	−7.53	6.84 ± 1.10	7.96
2020	2.77 ± 0.43	−1.51	1.41 ± 0.65	8.65	6.84 ± 1.16	0.05
2021	2.68 ± 0.42	−2.94	1.29 ± 0.64	−8.31	6.75 ± 1.25	−1.39
2022	2.58 ± 0.39	−3.88	1.65 ± 0.77	27.09	6.26 ± 0.74	−7.21
Mean	2.75 ± 0.47	−2.67 ± 2.88	1.42 ± 0.72	2.52 ± 12.48	6.69 ± 1.12	−3.48 ± 7.26

Unit of the total column is molecules cm⁻². The unit of annual variation is yr⁻¹. Mean ± standard deviation.

lists the mean and annual variation of the total column for CO, H₂CO, and HCN. The mean total columns of CO, H₂CO, and HCN from 2016 to 2022 are (2.75 ± 0.47) × 10¹⁸ molecules cm⁻², (1.42 ± 0.72) × 10¹⁶ molecules cm⁻², and (6.69 ± 1.12) × 10¹⁵ molecules cm⁻², respectively. The mean annual variation rates for CO, H₂CO, and HCN are (−2.67 ± 2.88)% yr⁻¹, (2.52 ± 12.48)% yr⁻¹, and (−3.48 ± 7.26)% yr⁻¹ from 2016 to 2022, respectively. So, CO and HCN gradually decreased, and H₂CO slowly increased. However, the mean of the CO and HCN columns increased from 2018 to 2019, with an increasing rate of 2.40% and 7.96%, respectively. H₂CO shows a strong year-to-year growth from 2021 to 2022, and the variation rate is 27.09%.

The FTIR spectrometer in Toronto collected solar absorption spectra for the retrieval of the time series of the total columns of CO, HCN, and other gases. CO exhibited lower levels during summer and fall as part of its annual cycle, while HCN peaked in May as part of its own annual pattern. During July and August, the HCN column displayed higher standard deviations, attributed to increased biomass burning, which results in skewed mean values [44]. In Bremen, the daily average of the CO total column reached its peak in February–March, with the lowest point in July–September. The daily average of HCN reached its highest levels in August–September and its lowest in December–January [45]. The total column of CO at Eureka peaked at 2.20 × 10¹⁸ molecules cm⁻² in March and reached its lowest point at 1.56 × 10¹⁸ molecules cm⁻² in September. The seasonal amplitude of the CO total column was 34%. The total column of HCN and H₂CO exhibited a seasonal variation, peaking in summer and reaching their lowest levels in winter, with seasonal amplitudes of 78% and 93%, respectively [6]. The relative annual variations of CO, H₂CO, and HCN in the Xianghe site from June 2018 to November 2021 were −2.2 ± 2.0% yr⁻¹, −6.7 ± 4.0% yr^−1, and 1.2 ± 2.3% yr⁻¹, respectively [32].

The seasonal variations for CO in Hefei are similar to those in Toronto and Eureka, exhibiting higher concentrations during winter and lower concentrations during summer. This was related to increased heating and traffic emissions in winter [6,11,44]. The H₂CO and HCN in Hefei and Eureka exhibit similar seasonal variations, with higher levels during summer and lower during winter, mainly due to more active photochemical reactions and increased biomass burning in summer [6]. In addition, high biogenic emissions from vegetation and forests also contribute to the high levels of H₂CO in summer. The annual variations in CO and HCN show a gradual decrease in Hefei and Xianghe, possibly due to the increased use of clean energy and the implementation of environmental protection measures [32]. H₂CO shows a decrease in Xianghe, reflecting changes in industrial and traffic emission sources in this region [32]. The seasonal and annual variations of CO, H₂CO, and HCN at each site are influenced by a combination of local climatic conditions, emission sources, and policy changes.

3.2. Enhancement Ratios of H₂CO and HCN Relative to CO during Biomass-Burning Period

The total column of CO and H₂CO at the Hefei station for all years and each individual year from 2016 to 2022 are plotted against the total column of HCN, as shown in Figure 9. We utilized the least-squares method described by York et al., (2004) to fit the coincident measurements with a linear regression equation [46].

Table 5. Correlation R value, slope, and intercept between CO and H₂CO with HCN in each year and all years from 2016 to 2022 at the Hefei site.

	CO			H2CO
Year	R	Slope	Intercept (×1018)	R	Slope	Intercept (×1015)
2016	0.64	264.78 ± 36.89	0.90 ± 0.29	0.12	0.22 ± 0.23	5.89 ± 1.83
2017	0.11	68.81 ± 56.80	2.58 ± 0.36	0.52	1.96 ± 0.25	−3.04 ± 1.68
2018	0.46	207.77 ± 25.77	1.43 ± 0.17	0.49	1.88 ± 0.22	−1.22 ± 1.43
2019	0.27	97.86 ± 23.13	2.09 ± 0.16	0.72	3.08 ± 0.20	−10.90 ± 1.39
2020	0.32	112.40 ± 28.01	2.05 ± 0.19	0.58	1.96 ± 0.25	−3.09 ± 1.68
2021	0.46	131.84 ± 18.03	1.87 ± 0.13	0.62	2.19 ± 0.19	−4.39 ± 1.33
2022	0.30	155.34 ± 45.29	1.67 ± 0.29	0.70	3.95 ± 0.38	−14.52 ± 2.38
2016–2022	0.37	136.95 ± 10.28	1.88 ± 0.07	0.47	1.68 ± 0.09	−1.09 ± 0.64

Regression line slope ± standard deviation. Intercept ± standard deviation.

shows the correlation R values, slopes, and intercepts between CO and H₂CO with HCN in each year and all years at the Hefei site from 2016 to 2022.

Good correlations between the gases indicate that these gas molecules undergo similar processes of production and dilution [7]. HCN, CO, and H₂CO are recognized as primary species from fire-induced biomass burning [5]. Biomass burning is the predominant source of HCN [21,22,29,47], making HCN a reliable indicator of biomass-burning occurrence. If biomass burning predominantly affects the variability of CO and H₂CO, a high correlation of CO and H₂CO with HCN should appear, and the reverse is also true [24,48]. For the observation span of 2016 to 2022, the correlation R values between CO and H₂CO with HCN in all years are 0.37 and 0.47, respectively, showing a weak correlation. For each year, the highest R value between CO and HCN occurred in 2016 (R = 0.64), while the highest R value between H₂CO and HCN occurred in 2019 (R = 0.72). Most correlation R values between H₂CO with HCN are higher than those between CO and HCN in each year. So, biomass-burning emissions contribute more to atmospheric H₂CO throughout the observation period.

Further, to clarify how biomass burning affects total column changes in CO and H₂CO, the correlation between CO and H₂CO with HCN in each month at the Hefei site from 2016 to 2022 was analyzed. The results are displayed in

Table 6. Monthly correlation R value between CO and H₂CO with HCN from 2016 to 2022 at the Hefei site. Blue values are those with strong correlations (R value ≥ 0.80).

		1	2	3	4	5	6	7	8	9	10	11	12
2016	CO	0.68	0.83	0.44	0.90	0.27						0.63	0.64
	H2CO	0.43	0.83	0.25	0.12	0.03						0.47	0.35
2017	CO	0.68	0.48	0.55	0.21	0.85					0.20	0.12	0.86
	H2CO	0.82	0.26	0.21	0.26	0.85					0.20	0.68	0.88
2018	CO			0.16	0.83	0.98				0.84	0.81	0.11	0.72
	H2CO			0.19	0.82	0.77				0.12	0.81	0.35	0.18
2019	CO	0.67		0.66	0.46	0.29	0.93			0.83	0.81	0.88	0.82
	H2CO	0.11		0.30	0.81	0.14	0.94			0.09	0.82	0.82	0.82
2020	CO		0.30	0.36	0.81	0.06				0.17	0.54	0.21	0.82
	H2CO		0.58	0.63	0.82	0.42				0.06	0.31	0.32	0.68
2021	CO	0.20	0.37	0.89	0.87	0.20	0.42				0.37	0.42	0.29
	H2CO	0.16	0.34	0.76	0.11	0.58	0.28				0.39	0.74	0.37
2022	CO	0.24	0.92	0.39	0.32	0.44					0.82	0.37	0.96
	H2CO	0.24	0.31	0.32	0.46	0.44					0.81	0.38	0.88

. Monthly correlation coefficient R values exceeding 0.8 for CO with HCN are observed in February and April 2016; May and December 2017; April, May, September, and October 2018; June and September to December 2019; April and December 2020; March and April 2021; and February, October, and December 2022. For H₂CO with HCN, the monthly correlation coefficient R values greater than 0.8 are found in February 2016; January, May, and December 2017; April and October 2018; April, June, and October to December 2019; April 2020; and October and December 2022. Here correlation coefficient R values greater than 0.8 are regarded as strong correlations. It can be reasonably assumed that the variability of the gases may be dominated by biomass burning in the corresponding month.

Fires emit heat energy, which spreads through radiation, conduction, and convection. Fire radiative energy (FRE), similar to electromagnetic radiation, travels through space and is detectable from aircraft and satellites [49]. Retrieving fire radiative power (FRP) provides new avenues for studying emissions from biomass burning and their impact on air quality [50,51]. For each fire pixel detected by satellite, the corresponding FRP (or FRE) can be obtained. FRP represents the pixel-integrated fire radiative power in megawatts (MW). The Fire Information for Resource Management System (FIRMS) archives FRP data, which is generated from the Visible Infrared Imaging Radiometer Suite (VIIRS) by NASA (https://firms.modaps.eosdis.nasa.gov/download/, accessed on 2 April 2024). Figure 10 shows the FRP values measured by satellite in Anhui province from 2016 to 2022. The total FRP values in each month are calculated, shown in Figure 10b, and the months with the total FRP greater than the monthly average within each year are marked with red.

The months in which the correlation coefficient between CO and H₂CO with HCN exceeds 0.8 are divided into two categories. In the first category, the correlation between CO or H₂CO with HCN both exceeds 0.8 in these months. The first category includes February 2016; May and December 2017; April and October 2018; June, October, November, and December 2019; April and December 2020, and October and December 2022. In the second category, the correlation between CO or H₂CO with HCN exceeds 0.8 for only one gas. The second category comprises April 2016, January 2017, May and September 2018, April and September 2019, December 2020, March and April 2021, and February 2022. In the first category, it is found that the total FRP for all months is greater than the monthly average in each year. This suggests the biomass-burning occurrence in Anhui province for the months with high total FRP values. So, the main driving factor for the variation of CO and H₂CO is biomass-burning emissions in this category. In the second category, the total FRP values for these months are all lower than the annual monthly average. The pattern with one gas of CO or H₂CO showing a high correlation with HCN, but with low FRP means that CO or H₂CO are affected by long-distance biomass-burning sources, rather than the sources from Anhui province.

The monthly mean deviations of gas (ΔCO, ΔH₂CO, and ΔHCN) are obtained by removing the monthly means from the individual total column of CO, H₂CO, and HCN. The monthly mean deviations reduce the influence of the atmospheric background and remove the seasonal component [24,30,32]. During the months when the variations of H₂CO and CO are predominantly affected by local emissions from biomass burning (in the first category), the relationship between ΔH₂CO and ΔHCN with ΔCO is shown in Figure 11. The specific correlation coefficients (R), slopes, and intercepts between ΔH₂CO and ΔHCN with ΔCO are listed in

Table 7. Monthly correlation R value, slope (EnhR), and intercept between ΔH₂CO and ΔHCN versus ΔCO for months when H₂CO and CO are predominantly influenced by biomass-burning emissions.

Date	ΔH2CO/ΔCO			ΔHCN/ΔCO
	R	Slope (EnhR)	Intercept	R	Slope (EnhR)	Intercept
February 2016	0.91	0.18 ± 0.02	2.06 ± 0.97	0.91	0.18 ± 0.02	2.06 ± 0.97
May 2017	0.89	1.02 ± 0.09	−1.50 ± 3.43	0.89	0.25 ± 0.09	6.72 ± 2.76
December 2017	0.93	0.52 ± 0.05	1.30 ± 1.27	0.86	0.08 ± 0.02	−3.26 ± 0.93
April 2018	0.81	0.51 ± 0.05	−9.22 ± 2.53	0.83	0.22 ± 0.02	−1.63 ± 1.00
October 2018	0.83	0.59 ± 0.05	7.40 ± 2.82	0.80	0.10 ± 0.01	−0.49 ± 0.62
June 2019	0.82	1.42 ± 0.15	11.74 ± 4.52	0.93	0.30 ± 0.07	16.21 ± 3.57
October 2019	0.76	0.67 ± 0.10	7.57 ± 3.37	0.79	0.24 ± 0.05	1.80 ± 1.40
November 2019	0.81	0.74 ± 0.08	−6.85 ± 3.48	0.88	0.13 ± 0.01	−0.26 ± 0.69
December 2019	0.83	0.73 ± 0.06	4.92 ± 2.57	0.83	0.10 ± 0.01	−2.07 ± 0.43
April 2020	0.82	0.84 ± 0.09	−7.52 ± 3.08	0.88	0.28 ± 0.04	4.72 ± 1.37
October 2022	0.80	1.01 ± 0.13	−19.44 ± 5.70	0.82	0.34 ± 0.07	7.59 ± 1.70
December 2022	0.93	0.50 ± 0.08	0.51 ± 2.43	0.96	0.31 ± 0.04	1.71 ± 1.24
All	0.76	0.70 ± 0.03	−0.38 ± 1.18	0.73	0.13 ± 0.01	0.16 ± 0.36

Regression line slope ± standard deviation, Units in EnhR are percent (%). The intercept of ΔH₂CO/ΔCO and ΔHCN/ΔCO is × 10¹⁴, and the intercept ± standard deviation.

. The enhancement ratio (EnhR), defined as the slope of ΔH₂CO/ΔCO and ΔHCN/ΔCO, is a useful metric for identifying the emissions of biomass burning [25,52,53,54]. When the R values for both H₂CO and CO with HCN are greater than 0.8, ΔH₂CO and ΔHCN with ΔCO also exhibit a high correlation. The overall correlation R values for ΔH₂CO and ΔHCN with ΔCO are 0.76 and 0.73, respectively. The monthly R values range between 0.76 and 0.93 for ΔH₂CO with ΔCO, and between 0.79 and 0.96 for ΔHCN with ΔCO. The calculated EnhR values for ΔH₂CO/ΔCO and ΔHCN/ΔCO are in the range of 1.8 × 10⁻³ to 14.2 × 10⁻³ and 0.8 × 10⁻³ to 3.4 × 10⁻³, respectively.

Additionally, for the months in the second category when the variations of H₂CO and CO are influenced by long-distance biomass burning, Figure 12 illustrates the relationship between ΔH₂CO and ΔHCN with ΔCO. Detailed values can be found in

Table 8. Monthly correlation R value, slope (EnhR), and intercept between ΔH₂CO and ΔHCN versus ΔCO for months in the second category when H₂CO or CO are affected by long-distance biomass burning sources, “/” means that the slope and intercept were not calculated.

Date	ΔH2CO/ΔCO			ΔHCN/ΔCO
	R	Slope (EnhR)	Intercept	R	Slope (EnhR)	Intercept
April 2016	0.83	0.34 ± 0.07	−8.39 ± 3.38	0.51	/	/
January 2017	0.68	0.42 ± 0.09	−5.43 ± 3.41	0.68	0.09 ± 0.03	−1.91 ± 0.97
May 2018	0.86	3.01 ± 0.73	8.36 ± 4.86	0.98	0.40 ± 0.06	0.59 ± 0.38
September 2018	0.59	/	/	0.84	0.35 ± 0.08	7.48 ± 1.67
April 2019	0.57	/	/	0.52	/	/
September 2019	0.82	0.96 ± 0.09	−23.43 ± 4.40	0.76	1.17 ± 0.58	31.63 ± 17.13
December 2020	0.89	0.55 ± 0.05	−5.46 ± 2.96	0.77	0.08 ± 0.02	−0.17 ± 0.90
March 2021	0.85	0.62 ± 0.06	−3.63 ± 2.56	0.89	0.40 ± 0.03	−4.33 ± 1.16
April 2021	0.28	/	/	0.87	0.23 ± 0.02	−2.66 ± 0.68
February 2022	0.33	/	/	0.92	0.19 ± 0.02	0.78 ± 0.48
All	0.78	0.63 ± 0.04	−8.41 ± 1.78	0.71	0.20 ± 0.02	−0.74 ± 0.59

Regression line slope ± standard deviation, Units in EnhR are percent (%). The intercept of ΔH₂CO/ΔCO and ΔHCN/ΔCO is × 10¹⁴, and the intercept ± standard deviation.

. In the months when the R value of only one gas, H₂CO or CO, with HCN is greater than 0.8, some correlation R values between ΔH₂CO and ΔHCN with ΔCO are low values. Therefore, the months with correlation R values between ΔH₂CO or ΔHCN with ΔCO below 0.6 were excluded from the analysis, and the enhancement ratio was not calculated. Then the overall R values between ΔH₂CO and ΔHCN with ΔCO were 0.78 and 0.71, respectively. The monthly R values for ΔH₂CO and ΔCO ranged from 0.68 to 0.89, and for ΔHCN and ΔCO from 0.68 to 0.98. The EnhR for ΔH₂CO/ΔCO and ΔHCN/ΔCO are in the range of 3.4 × 10⁻³ to 30.1× 10⁻³ and in the range of 0.8 × 10⁻³ to 11.7 × 10⁻³, respectively. The EnhR of ΔH₂CO/ΔCO in May 2018 and ΔHCN/ΔCO in September 2019 showed abnormally large values. After removing these outliers, The EnhR ranges from 3.4 × 10⁻³ to 9.6 × 10⁻³ and from 0.8 × 10⁻³ to 4.0 × 10⁻³, respectively.

The EnhRs of ΔH₂CO/ΔCO and ΔHCN/ΔCO from the FTIR measurements at Xianghe during 2018 to 2021 were 3.7–6.8 × 10⁻³ and 0.5–0.9 × 10⁻³, respectively [32]. The EnhR of H₂CO and HCN relative to CO in Hefei is slightly larger than that in Xianghe. The reason for this difference may be that we only consider the months when biomass burning dominated the gas changes in this study. The HCN/CO ratios measured in Hefei, which are similar to the range of 0.2–7.1 × 10⁻³ reported by Yokelson et al. (1997) and 0.4–2.6 × 10⁻³ reported by Holzinger et al., (1999), are consistent with laboratory measurements [47,55].

3.3. Analysis of Air Mass Transport

The Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model provides effective methods for analyzing the transport and dispersion of pollutants through air masses [56]. HYSPLIT provides a comprehensive system for studying the atmospheric dispersion and transport of diverse pollutants across different regions, utilizing meteorological fields from the Global Data Assimilation System (GDAS) [57]. To comprehend the influence of air mass transport on the variations of the gases over the Hefei site during the periods when the biomass burning occurred, we employed the HYSPLIT model to compute air mass trajectories backward for 24 h at 500 m. The results are shown in Figure 13. The months during which the monthly correlation R of CO and H₂CO with HCN is greater than 0.8 are included in the analysis of air mass transport.

The 24-h backward trajectories can be divided into five categories. The largest proportion of 26.39% was from the sea and passed through the northern part of Jiangsu province. In addition, 26.32% of air masses came from the southern part of Anhui province and 22.85% came from the eastern part of Jiangsu province and traveled through the southern part of Jiangsu province. Also, 16.48% of air masses came from the southern part of Henan province. Finally, the remaining 7.96% was from the Shanxi province and passed through the southern part of Hebei province, Henan province, and the northwest part of Anhui province. So, within 24 h, about 49.24% of air masses passed through Jiangsu province, and 26.32% came from the southern part of Anhui province. It means Jiangsu province, the eastern part, and the southern part of Anhui province had a great impact on the variations of pollutants over the Hefei site.

Further, the potential source contribution function (PSCF) of CO, H₂CO, and HCN in the Hefei site was calculated. The PSCF calculation has been applied in many studies to locate the potential source contribution areas associated with air pollutants [58,59]. Figure 14 shows the 24-h PSCF values of the three gases for the same months as in the analysis of airmass backward trajectories. Over a 24-h period, the areas with a high PSCF for CO are the southeastern part of Anhui province, the southern part of Zhejiang province, Shanghai, and Jiangsu province. The areas with a high PSCF for H₂CO are the southeastern part of Anhui province, the northern part of Anhui province, and the provinces bordering the southeast. The areas with a high PSCF for HCN are the eastern part of Anhui province, and the provinces bordering the southeast and northeast of Anhui. Overall, the biomass-burning emissions in the eastern part of Anhui province, the southeastern part of Anhui province, and the bordering provinces in the southeast of Anhui significantly affect the variations of the three gases. The pattern agrees with the 24-h backward trajectories of the air mass transport.

4. Conclusions

This study presents long-term data of total column and vertical profiles of atmospheric CO, H₂CO, and HCN at the Hefei site from 2016 to 2022, based on high-resolution FTIR measurements of solar absorption spectra. The seasonal and interannual variability of CO, H₂CO, and HCN from 2016 to 2022 are analyzed. During the observation period, atmospheric CO exhibited significant seasonal variations, characterized by high column concentrations observed during the spring and winter, and lower levels during the summer. The seasonal amplitude is 8.07 × 10¹⁷ molecules cm⁻², with a seasonal variability of 29.35% and an average annual variability rate of (−2.67 ± 2.88)% yr⁻¹. The H₂CO total column exhibited a seasonal pattern, showing higher levels in the summer and lower levels in the winter. The seasonal amplitude and variability of H₂CO are 1.89 × 10¹⁶ molecules cm⁻² and 133.07%, respectively. The average annual variability rate is (2.52 ± 12.48)% yr⁻¹. Similarly, HCN exhibited high column concentrations in the summer and low column concentrations in the winter. The seasonal amplitude is 2.32 × 10¹⁵ molecules cm⁻², with a seasonal variability of 34.69% and an average annual variability rate of (−3.48 ± 7.26)% yr⁻¹.

To evaluate the impact of biomass burning on the gas column variations, we utilized the correlation between atmospheric CO, H₂CO, and HCN columns to identify the months during which biomass burning influences the variations of the gases. The satellite-observed FRP values within the Anhui province are used to further find the months during which biomass burning occurred. The months during which the monthly R values between CO and H₂CO with HCN are greater than 0.8, and the monthly total FRP exceeds its monthly average, are considered biomass-burning occurrences in the Anhui province. Conversely, the months during which only one of the R between CO or H₂CO with HCN is greater than 0.8, and the monthly total FRP is below its monthly average, are regarded as being influenced by long-distance transport.

Then, the enhancement ratios (EnhR) represented as ΔH₂CO/ΔCO and ΔHCN/ΔCO for the months with biomass-burning occurrence and being influenced by the long-distance transport were calculated. For months with biomass-burning occurrence, the range of ΔH₂CO/ΔCO and ΔHCN/ΔCO was 1.8–14.2 × 10⁻³ and 0.8–3.4 × 10⁻³, respectively. For months being influenced by the long-distance transport, the range of ΔH₂CO/ΔCO and ΔHCN/ΔCO was 3.4–9.6× 10⁻³ and 0.8–4.0 × 10⁻³, respectively. Finally, the backward trajectory cluster analysis and PSCF calculation were conducted to examine air mass transport pathways and the potential source areas for the three gases at the Hefei site. The joint monitoring of atmospheric CO, H₂CO, and HCN in the Hefei area helps to identify biomass-burning months and seasons, demonstrating the capability of high-resolution FTIR technology to accurately monitor biomass-burning emissions.